Didn’t South Carolina explicitly state they were seceding from the union because of slavery?
Yes indeed, the sole argument stated as a cause for complaint in South Carolinas declaration was the conflict about Article IV of the Constitution, and it was cited by several other states too; and slavery was the stated issue across all the seceding states even where the constitutional point of Article IV was not cited.
The 2nd time they did. During the Nullification Crisis of 1830 it wasn’t the issue. The Nullification crisis was an attempt by South Carolina to refuse the laws of the National Government due to excessive tariffs by threatening secession. Tariffs were the continuing, burning, simmering, underlying issue. The slavery issue, to the South, was the ‘straw that broke the camel’s back’ by 1860.
AN ORDINANCE to dissolve the union between the State of South Carolina and other States united with her under the compact entitled “The Constitution of the United States of America.”
We, the people of the State of South Carolina, in convention assembled, do declare and ordain, and it is hereby declared and ordained, That the ordinance adopted by us in convention on the twenty-third day of May, in the year of our Lord one thousand seven hundred and eighty-eight, whereby the Constitution of the United States of America was ratified, and also all acts and parts of acts of the General Assembly of this State ratifying amendments of the said Constitution, are hereby repealed; and that the union now subsisting between South Carolina and other States, under the name of the “United States of America,” is hereby dissolved.
Done at Charleston the twentieth day of December, in the year of our Lord one thousand eight hundred and sixty.
Source: Official Records, Ser. IV, vol. 1, p. 1.